#14736: trig case where to_poly_solve True works, but not force
-----------------------------+------------------------
Reporter: kcrisman | Owner: burcin
Type: defect | Status: new
Priority: minor | Milestone: sage-6.4
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by kcrisman:
Old description:
> From the bug reporter spreadsheet and
> [https://groups.google.com/forum/?fromgroups#!topic/sage-
> support/oEgjsfBoK30 this sage-support thread]:
> {{{
> solve(sin(x)/cos(x)==1,x,to_poly_solve='force')
>
> This gives an empty list. I know it has at least one solution, namely
> pi/4.
> }}}
> Note that `to_poly_solve=True` does work.
New description:
From the bug reporter spreadsheet and
[https://groups.google.com/forum/?fromgroups#!topic/sage-
support/oEgjsfBoK30 this sage-support thread]:
{{{
solve(sin(x)/cos(x)==1,x,to_poly_solve='force')
This gives an empty list. I know it has at least one solution, namely
pi/4.
}}}
Note that `to_poly_solve=True` does work.
This is basically the same as [http://ask.sagemath.org/question/31191
/using-solve-with-trigonometric-functions/ this ask.sagemath question], by
the way.
{{{
sage: solve(tan(3*x)==1, x, to_poly_solve='force'
[]
}}}
We're basically silently failing since we can't translate `%solve` output
from Maxima.
{{{
(%i5) load(to_poly_solve);
Loading maxima-grobner $Revision: 1.6 $ $Date: 2009-06-02 07:49:49 $
(%o5) /Users/.../sage-6.9/local/share/maxima/5.35.1/share/t\
o_poly_solve/to_poly_solve.mac
(%i6) %solve(tan(3*x)=1,x);
2 %pi (12 %z11 + 1)
(%o6) %union(%if(3 tan (-----------------) - 1 # 0,
12
%pi
- 2 %pi %z11 - ---
6
[x = - ------------------], %union()),
2
2 2 %pi 2 %pi
%if(3 tan ((4 %pi %z7 - %i log(sin (---) + cos (---))
12 12
%pi %pi
(sqrt(3) + 1) sin(---) + (sqrt(3) - 1) cos(---)
12 12
+ 2 atan(-------------------------------------------------) + 2 %pi)/4) -
1 #
%pi %pi
(sqrt(3) - 1) sin(---) + (- sqrt(3) - 1) cos(---)
12 12
%pi %pi %pi
%pi
sqrt(3) sin(---) sin(---) sqrt(3) cos(---)
cos(---)
12 12 12
12 2
0, [x = - (%i (log((---------------- + -------- + ---------------- -
--------)
3/2 3/2 3/2
3/2
2 2 2 2
%pi %pi %pi %pi
sqrt(3) sin(---) sin(---) sqrt(3) cos(---) cos(---)
12 12 12 12 2
+ (---------------- - -------- - ---------------- - --------) )/2
3/2 3/2 3/2 3/2
2 2 2 2
%pi %pi %pi %pi
sin(---) cos(---) cos(---) sin(---)
12 12 12 12
sqrt(3) (-------- + --------) -------- - --------
sqrt(2) sqrt(2) sqrt(2) sqrt(2)
----------------------------- - -------------------
2 2
+ %i (atan(---------------------------------------------------) + %pi))
%pi %pi %pi %pi
sin(---) cos(---) sin(---) cos(---)
12 12 12 12
sqrt(3) (-------- - --------) -------- + --------
sqrt(2) sqrt(2) sqrt(2) sqrt(2)
----------------------------- - -------------------
2 2
2
- 2 %pi %z7)/2], %union()), %if(3 tan ((4 %pi %z9
%pi %pi
(sqrt(3) - 1) sin(---) + (sqrt(3) + 1) cos(---)
12 12
+ 2 atan(-----------------------------------------------)
%pi %pi
(sqrt(3) + 1) sin(---) + (1 - sqrt(3)) cos(---)
12 12
2 %pi 2 %pi
- %i log(sin (---) + cos (---)))/4) - 1 # 0,
12 12
%pi %pi %pi
%pi
sqrt(3) sin(---) sin(---) sqrt(3) cos(---)
cos(---)
12 12 12 12
2
[x = - (%i (log((- ---------------- + -------- - ---------------- -
--------)
3/2 3/2 3/2 3/2
2 2 2 2
%pi %pi %pi %pi
sqrt(3) sin(---) sin(---) sqrt(3) cos(---) cos(---)
12 12 12 12 2
+ (- ---------------- - -------- + ---------------- - --------) )/2
3/2 3/2 3/2 3/2
2 2 2 2
%pi %pi %pi %pi
sin(---) cos(---) cos(---) sin(---)
12 12 12 12
sqrt(3) (-------- + --------) -------- - --------
sqrt(2) sqrt(2) sqrt(2) sqrt(2)
+ %i atan2(- ----------------------------- - -------------------,
2 2
%pi %pi %pi %pi
sin(---) cos(---) sin(---) cos(---)
12 12 12 12
-------- + -------- sqrt(3) (-------- - --------)
sqrt(2) sqrt(2) sqrt(2) sqrt(2)
- ------------------- - -----------------------------)) - 2 %pi %z9)/2],
2 2
%union()))
}}}
--
--
Ticket URL: <http://trac.sagemath.org/ticket/14736#comment:5>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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